{VERSION 6 0 "IBM INTEL NT" "6.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 1" -1 3 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 4 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Ti mes" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 } {PSTYLE "Maple Output" -1 12 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Plot " -1 13 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 } 3 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "?plot" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "plot([sin, cos], -Pi .. Pi);" }} {PARA 13 "" 1 "" {GLPLOT2D 494 494 494 {PLOTDATA 2 "6&-%'CURVESG6$7dw7 $$!0++tk#fTJ!#9$!0hSKD$z*G'!#B7$$!0v/29e&3JF*$!09%4!\\]GI$!#;7$$!0y]J* \\\")zIF*$!0j^4CPQ<'F37$$!0PuvJ!\\ZIF*$!0r=:U^jR*F37$$!0`lIP^\\,$F*$!0 nqVRIIE\"!#:7$$!0+![!3nD)HF*$!0zyJ]hNe\"FC7$$!0AvdpUD&HF*$!0!3PW'e#z=F C7$$!0k$\\%=a9#HF*$!0\\gi_ZO=#FC7$$!0m`;S-$*)GF*$!0fj,iBi\\#FC7$$!0,*) *HPDdGF*$!0+dB!)H_!GFC7$$!0V**=t(GCGF*$!0x*3v:2?JFC7$$!0OQGE^_z#F*$!0I U^A(e%R$FC7$$!0fWf2jDw#F*$!0U/)z4>+PFC7$$!0\"[@o1uHFF*$!0m&zx82.SFC7$$ !0#H_'>5\")p#F*$!09:tMw3H%FC7$$!0Mtzp'QpEF*$!0s/$>%>&[XFC7$$!0i,+oJ_j# F*$!09^B\"3)*\\[FC7$$!0]e'**yH1EF*$!01!Q[e%45&FC7$$!0&)=Z.TEd#F*$!0'=X #>\"\\(Q&FC7$$!0(4J1!\\Ga#F*$!01,S:^gj&FC7$$!0-l$HC;5DF*$!0r]]:)*H!fFC 7$$!0Q5%yq.zCF*$!0IN>KP8:'FC7$$!0$H&*R5cYCF*$!0_>=?(4/kFC7$$!0+F()*yt; CF*$!0)on(>n-j'FC7$$!0R[>hpXQ#F*$!0d9(*)egnoFC7$$!0r#F*$!0g5zq>+6)FC7$$!0xqkj?;;#F*$!0'=rIy\"[I)FC7$$!0Reg#>(48#F*$!0nh/A =;Z)FC7$$!0\"p&e)yC)4#F*$!0c;@*e#4k)FC7$$!0n&oT]fo?F*$!0oj5(yN'y)FC7$$ !0*Rm]mF *$!0!4xW_\"*)>*FC7$$!0lGN#ehU>F*$!0`agWymJ*FC7$$!0t'*Qa!)*4>F*$!0$Gi[S EI%*FC7$$!0>;3*)[&y=F*$!008'Rw;I&*FC7$$!05nd[0k%=F*$!0`'>QgfA'*FC7$$!0 oSVCGX\"=F*$!0hMIETWq*FC7$$!0,7,PO_y\"F*$!0wEN1d4x*FC7$$!0lfmdk;v\"F*$ !0Fcczyo$)*FC7$$!0g$Qkvj@zL9h**FC7$$!0W;zXb\\i\"F*$!0lg]p***FC7$$!0&HV&>_?c\"F*$!0]pKq<'****FC7$$!0yL/ \"[dJ:F*$!0PU#\\$4B***FC7$$!0Dd4MP#)\\\"F*$!0!*)3:vot**FC7$$!06)zUFZp9 F*$!0cG%e:r[**FC7$$!0nAJA8nV\"F*$!0&QC+KC5**FC7$$!0)yQW\"p]S\"F*$!0+`9 `')H')*FC7$$!0?kztXMP\"F*$!0M=C%\\*e!)*FC7$$!0HZ$o'Q>M\"F*$!0#ycy=ER(* FC7$$!0/&4Q-n68F*$!0X\"zYF9m'*FC7$$!0P$Rj#\\*y7F*$!0-3LpSrd*FC7$$!0=J> !QwZ7F*$!0\"z[R7x#[*FC7$$!0r>AdU\\@\"F*$!07qE!R\\t$*FC7$$!0IndXJ_=\"F* $!0')yMUheE*FC7$$!0E,,6&R_6F*$!0sJm$pRP\"*FC7$$!0F!*GhV47\"F*$!0,3'p:6 0!*FC7$$!0x.&p'o&*3\"F*$!0*=OzMFk))FC7$$!0%=`>uzc5F*$!0Cz!RhE5F*$!0T%)o]3bb)FC7$$!0JWC^=q&**FC$!0fVe>49R)FC7$$!0^?Bu7dh*FC$! 0MR&Qr\"4?)FC7$$!0m*yB$)o1$*FC$!0U:G7'>?!)FC7$$!0(>RsHl!**)FC$!04V(paX FyFC7$$!0)[_gJDp')FC$!0ttX*oUBwFC7$$!0S!*4>CQP)FC$!0Fd(HV$*GuFC7$$!06v hZ1*e!)FC$!0Xq)[nZ9sFC7$$!0hva$fQYxFC$!0$=%GLyX*pFC7$$!0\"o3+h37uFC$!0 `IUR*z^nFC7$$!0m#=x43q%FC7$$!07bm8ice%FC$!0%=eK!HmU%FC7$$!0H eI&yD]UFC$!0,(=IFWBTFC7$$!0EZ`*)R+'RFC$!0E9gtYt&QFC7$$!0d%)*>SrEOFC$!0 iV'*HJxa$FC7$$!0.CO7K+u\"FC$\"0y7Wj_7t\"FC7$$\"0=TfhiQ1#FC$\"0z:^)> C\\?FC7$$\"00*)HY1TO#FC$\"0(*Q9FY@M#FC7$$\"0![!ed\"*\\n#FC$\"04P'fO?VE FC7$$\"0e/US4l*HFC$\"0B9J>n=&HFC7$$\"02^37'*pJ$FC$\"0OCfk/lD$FC7$$\"0* ou,hlYOFC$\"0)*\\/8pjc$FC7$$\"0gdBz?q$RFC$\"0?[h)))4OQFC7$$\"0K&HhE!RE %FC$\"0dN:ppe8%FC7$$\"02$fQn7#f%FC$\"0ee)Q[UKWFC7$$\"0,7bXJ%3\\FC$\"0 \"yCelp8ZFC7$$\"0$y+Tkm&>&FC$\"0e\"Qm,/l\\FC7$$\"0'\\s?m@PbFC$\"0M-)*4 k&e_FC7$$\"0?cTUal#eFC$\"0(H@/=V-bFC7$$\"0r_N2BJ;'FC$\"0X](H))H!y&FC7$ $\"0aJwNV5Y'FC$\"0Xw=Y03-'FC7$$\"0'44F\"4zy'FC$\"0E=M6C&yiFC7$$\"0WPmj i\"*4(FC$\"0/8Hm-x^'FC7$$\"0'=@@I#RU(FC$\"0w;L?E0w'FC7$$\"0BrMVa@s(FC$ \"0k?O>Ss(pFC7$$\"0Id7IPQ/)FC$\"0j3diLS?(FC7$$\"02kNRvzP)FC$\"0[a[a7M A$**FC$\"0nq$**G!zP)FC7$$\"0N.cqKt-\"F*$\"0P()ynF#f&)FC7$$\"0u:gT\")z0 \"F*$\"0vcPwoOr)FC7$$\"0@G1@kS(*FC7$$\"0XLx4DWP\"F*$\"0!G7!\\5y!)*FC7$$ \"06i>(pr.9F*$\"0C$=Uoug)*FC7$$\"0Z9aw)GP9F*$\"0,ZN&4,6**FC7$$\"0_!pxd Jn9F*$\"0pg-k1l%**FC7$$\"0xwb$3L*\\\"F*$\"0x\"f%GuW(**FC7$$\"0E.5Lt*H: F*$\"0B3Ado;***FC7$$\"0odT)y*Rc\"F*$\"0iyn!*o(****FC7$$\"0)R8Z1Y$f\"F* $\"0#p&GvJu***FC7$$\"0=Tm9,pi\"F*$\"0\"**)RPlU)**FC7$$\"0MS;`ytl\"F*$ \"01k'=5ai**FC7$$\"0(o6,gr!p\"F*$\"0o^h[#=G**FC7$$\"0,w#*f![>%)Qy\"F*$\"0]xvb DQx*FC7$$\"0#*4Tg2b\"=F*$\"03$\\gJ2-(*FC7$$\"0$ostY,Z=F*$\"0wa.XO4i*FC 7$$\"03zR5$Gx=F*$\"0Z&[%H%*R`*FC7$$\"0v!oyS+5>F*$\"0Ys:u&=I%*FC7$$\"0& H9S&*=T>F*$\"0%G=:3&=K*FC7$$\"0Ta)p2,u>F*$\"04sduW!)>*FC7$$\"0#oI')=s. ?F*$\"0.L?\"GUx!*FC7$$\"0'G(>Bel.#F*$\"0iRb]'zM*)FC7$$\"0&Q=H(4!o?F*$ \"0XW&*=^\"*y)FC7$$\"0NqDn%Q*4#F*$\"0Qw')[)>N')FC7$$\"0GUD#f:K@F*$\"0% [k'H@`Y)FC7$$\"0VB,WRB;#F*$\"0(p8?;\"3I)FC7$$\"0pH3\\^K>#F*$\"0^r]o%\\ C\")FC7$$\"02Uy1#QFAF*$\"0u6gi43#zFC7$$\"0;&p4XGeAF*$\"0sOJXC%GxFC7$$ \"0#\\$[/)))*G#F*$\"0<*\\hK/CvFC7$$\"0j@g-G?K#F*$\"0uh8S([3tFC7$$\"03v H#4d^BF*$\"0c7Cn&o.rFC7$$\"0hcWpiIQ#F*$\"0p.bi^&yoFC7$$\"0cE&[ZJ9CF*$ \"0\\qNJ(Q[mFC7$$\"0Wl?tWxW#F*$\"0F?gc,]R'FC7$$\"0'eNW_CxCF*$\"0p>umaa ;'FC7$$\"0O3:r#G6DF*$\"0:#o8<&R*eFC7$$\"0UO9!*)*>a#F*$\"0AW*f82VcFC7$$ \"00Je'4RsDF*$\"0hl*pxf*Q&FC7$$\"0P'f)>s]g#F*$\"0&)oL\\%[6^FC7$$\"0&\\ oLc)yj#F*$\"0]+0`an#[FC7$$\"0(4-,5unEF*$\"0xW%)GpJc%FC7$$\"00h\\2Y%*p# F*$\"0*ePGg!)yUFC7$$\"0h3%GrQIFF*$\"0*3:.l9(*RFC7$$\"0HonbFRw#F*$\"0>s G=6vo$FC7$$\"0RRDN\\Hz#F*$\"09$*HYIiT$FC7$$\"0mv+%>GEGF*$\"0v;b\")=65$ FC7$$\"0s6ZK;w&GF*$\"0GMBE\\HF*$\"0QyZ3>2?#FC7$$\"0tc]/!Q^HF*$\"0&Q'=tw1*=FC7$$\"0f,hib \\)HF*$\"0x[u$H(*f:FC7$$\"0Z&3Y6u:IF*$\"0/R%=b>b7FC7$$\"0aetSIh/$F*$\" 0,X(R?tJ&*F37$$\"0q:v-;'yIF*$\"02k'>1]$H'F37$$\"0C<$H4.6JF*$\"0hDcp'pb IF37$$\"0+]/l#fTJF*$\"0l(pOMzRJF--%'COLOURG6&%$RGBG$\"*++++\"!\")$\"\" !FejnFdjn-F$6$7dw7$F($!\"\"Fejn7$F/$!0My45WX***FC7$F5$!0wX:nB4)**FC7$F :$!00U_Tcd&**FC7$F?$!0;yr/<*>**FC7$FE$!0Odge?Q()*FC7$FJ$!0m)Qe@$=#)*FC 7$FO$!0ji\">Ane(*FC7$FT$!0kXrjKMo*FC7$FY$!0dF]4t%)f*FC7$Fhn$!0f?@^(z+& *FC7$F]o$!09a>_4iS*FC7$Fbo$!0*fkx9C!H*FC7$Fgo$!0X**zJ5Q;*FC7$F\\p$!0;B 8kGE.*FC7$Fap$!09*oE2n0*)FC7$Ffp$!0&)4'\\@:X()FC7$F[q$!04iD9$=,')FC7$F `q$!0jsW_iYU)FC7$Feq$!0sqY`V/E)FC7$Fjq$!0?!oI2%=2)FC7$F_r$!0*p*G(yA%)y FC7$Fdr$!0Kb\\cM.o(FC7$Fir$!0a*o7t&f[(FC7$F^s$!0H#=jo$)osFC7$Fcs$!05^0 I\\`.(FC7$Fhs$!0/&[lRpDoFC7$F]t$!0Ds\\!)zFf'FC7$Fbt$!0#f&G9F`M'FC7$Fgt $!0)H%o>un4'FC7$F\\u$!0q\\2?M/&eFC7$Fau$!0,sD'yXqbFC7$Ffu$!05S5n\\LJ&F C7$F[v$!07'>\"*)GL.&FC7$F`v$!0mNFC7$Fc]l$\"0 ZpW:^'oAFC7$Fh]l$\"0;&3Z\"fBc#FC7$F]^l$\"0)G2Nn@xGFC7$Fb^l$\"0uC!)*oVu JFC7$Fg^l$\"0:&R%e2R[$FC7$F\\_l$\"0JhQ)f#3w$FC7$Fa_l$\"07n=,,I1%FC7$Ff _l$\"0;g01H$[VFC7$F[`l$\"0W'oIvnGYFC7$F``l$\"0;CleLm\"\\FC7$Fe`l$\"0^: \\'y=x^FC7$Fj`l$\"037TrS\"RaFC7$F_al$\"0Xt,/@Bs&FC7$Fdal$\"0L'Q#*p(H(f FC7$Fial$\"0`$[W(=MA'FC7$F^bl$\"0L0YlN&)FC7$Feel$\"0F!))Q:;s')FC7 $Fjel$\"0#QWVkkD))FC7$F_fl$\"0X'4I5)o'*)FC7$Fdfl$\"06P$35G5\"*FC7$Fifl $\"0nc%ev4E#*FC7$F^gl$\"0C&\\$*FC7$Fcgl$\"0?D#pC3c%*FC7$Fhgl$\"0() \\iDiCb*FC7$F]hl$\"0[hOt4(R'*FC7$Fbhl$\"0U)4z%>\">(*FC7$Fghl$\"0F!H[_k #z*FC7$F\\il$\"0\"f`iBO])*FC7$Fail$\"0j(R,8=)*)*FC7$Ffil$\"08;f6!>R**F C7$F[jl$\"063l%elp**FC7$F`jl$\"0)4(\\W\"3))**FC7$Fejl$\"0JA9Uo*)***FC7 $Fjjl$\"0')R0\\_*)***FC7$F_[m$\"0E&[]UQ))**FC7$Fd[m$\"0aY1Y+x'**FC7$Fi [m$\"0h%e&>.0%**FC7$F^\\m$\"0d3a\"y5+**FC7$Fc\\m$\"0fqw8)**[)*FC7$Fh\\ m$\"07L`Yyxy*FC7$F]]m$\"0\"oJZ\"\\=s*FC7$Fb]m$\"0&\\\\^$\\Vk*FC7$Fg]m$ \"0fA3&eRa&*FC7$F\\^m$\"0K$R*H-\\X*FC7$Fa^m$\"0C%\\\"pICM*FC7$Ff^m$\"0 vAKP_\\B*FC7$F[_m$\"0ma2))FC7$Fj_m$\"0&yATUM!o)FC7$F_`m$\"0l7EdLd])FC7$Fd`m$\"0n\\^cW+N)FC7$F i`m$\"0CB!pf:g\")FC7$F^am$\"0)\\n[NN%)zFC7$Fcam$\"06g&eTK$y(FC7$Fham$ \"0ZN]bkTe(FC7$F]bm$\"0'y*pYL&otFC7$Fbbm$\"0]%p3mmjrFC7$Fgbm$\"0.ceH`b $pFC7$F\\cm$\"0wf!GD,\"p'FC7$Facm$\"0x\\f)y/skFC7$Ffcm$\"0JR%*p:%HiFC7 $F[dm$\"0)4$p.+B(fFC7$F`dm$\"01:r$Qn9dFC7$Fedm$\"0s!Q?:#*faFC7$Fjdm$\" 0u3szO5<&FC7$F_em$\"0\"Gru+K1\\FC7$Fdem$\"0YePv(f=YFC7$Fiem$\"0l#z>\"* f`VFC7$F^fm$\"0zti09&fSFC7$Fcfm$\"0ky]#>!*yPFC7$Fhfm$\"0z3FUF=[$FC7$F] gm$\"0SbOyez=$FC7$Fbgm$\"0IQ$Q8*p(GFC7$Fggm$\"0%fMnBfuDFC7$F\\hm$\"0\" R!Gp%\\Mf6^>FC7$Ffhm$\"0)3.j;FC7$F[im$\"0!3]AI6J8F C7$F`im$\"0:%4e'fH.\"FC7$Feim$\"07)y$Rn/9(F37$Fjim$\"0[vL!e;\"3%F37$F_ jm$\"0D)*zE!R)z'Fbdo7$Fdjm$!0kK`+QiE#F37$Fijm$!08zz/Rvg&F37$F^[n$!0EQ] %oSZ')F37$Fc[n$!0sf()eCj>\"FC7$Fh[n$!0pF=]q8[\"FC7$F]\\n$!0*\\U@&)\\/= FC7$Fb\\n$!0zHTM*y9@FC7$Fg\\n$!0d$HS@wACFC7$F\\]n$!0K[\"HI>FFFC7$Fa]n$ !0MJn+5r,$FC7$Ff]n$!0?`&>4SFLFC7$F[^n$!0fmb2?)>OFC7$F`^n$!0B2ZBqP#RFC7 $Fe^n$!0tY0[#G&>%FC7$Fj^n$!0jT]yO5\\%FC7$F__n$!0E***3@ypZFC7$Fd_n$!0] \"eE&[J/&FC7$Fi_n$!0]H1JwLK&FC7$F^`n$!0%4QcfUwbFC7$Fc`n$!0*[bChJIeFC7$ Fh`n$!0*Hmb/;/hFC7$F]an$!0=LIZzfM'FC7$Fban$!0%*e\\[:qe'FC7$Fgan$!0\\#e LYRDoFC7$F\\bn$!0!ys!z)HQqFC7$Fabn$!08?')pz%esFC7$Ffbn$!0KZw@p)puFC7$F [cn$!08p>m4zo(FC7$F`cn$!02!GYI>tyFC7$Fecn$!0<8vo[%y!)FC7$Fjcn$!07neJ\\ cD)FC7$F_dn$!0LSr,:LU)FC7$Fddn$!07?%[W#\\f)FC7$Fidn$!0q\\3'H*zv)FC7$F^ en$!0MGe=t\")*))FC7$Fcen$!00G\"pENQ!*FC7$Fhen$!0P!HHiRm\"*FC7$F]fn$!03 %Rn;G&H*FC7$Fbfn$!0Q-Gdq$)R*FC7$Fgfn$!0yZ&)o+q]*FC7$F\\gn$!0H[bi*[*f*F C7$Fagn$!0X>X;(z\"o*FC7$Ffgn$!0kq)=l$[v*FC7$F[hn$!0([5*fS'>)*FC7$F`hn$ !0Zab#[dx)*FC7$Fehn$!0(=ng9\"4#**FC7$Fjhn$!0XS.RpW&**FC7$F_in$!0VtfFw, )**FC7$Fdin$!0dK&o-L&***FC7$FiinFjjn-F^jn6&F`jn$\")Vyg>Fcjn$\")d@R!)Fc jnFb`q-%+AXESLABELSG6$Q!6\"Fi`q-%%VIEWG6$;$!+aEfTJ!\"*$\"+aEfTJFaaq%(D EFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curv e 1" "Curve 2" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "?trig" }}} {SECT 0 {PARA 3 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "1/2*exp(x) + 1/2*exp(-x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&#\"\"\"\"\"#F&-%$expG6#%\"xGF&F&*&#F&F'F&-F)6#,$%\" xG!\"\"F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "convert(" } {TEXT -1 31 "[LABEL REFERENCE NOT SUPPORTED]" }{MPLTEXT 1 0 7 ",trig); " }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "E1:=1/(2*I)*(exp(I*x) \+ -exp(-I*x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#E1G*&^##!\"\"\"\"# \"\"\",&-%$expG6#*&%\"xGF*^#F*F*F*-F-6#*&^#F(F*F0F*F(F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "convert(E1,trig);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$sinG6#%\"xG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "E3:=1/(2*I)*(exp(3*I*x) -exp(-3*I*x));" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%#E3G*&^##!\"\"\"\"#\"\"\",&-%$expG6#*&^#\"\"$F *%\"xGF*F*-F-6#*&^#!\"$F*F2F*F(F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "convert(E3,trig);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# -%$sinG6#,$*&\"\"$\"\"\"%\"xGF)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "?parametric" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "plot([sin(t), sin(3*t), t=0..2*Pi]);" }}{PARA 13 "" 1 "" {GLPLOT2D 494 494 494 {PLOTDATA 2 "6%-%'CURVESG6$7`x7$$\"\"!F)F(7$$\"0 2Wo')\\GI$!#;$\"0&4IEv8%*)*F-7$$\"0&4BBm$Q<'F-$\"0WD[/QF%=!#:7$$\"0e01 \"3N'R*F-$\"0]Z7c?dy#F57$$\"0%e-M..j7F5$\"0N5vD(\\3PF57$$\"0,OOWhNe\"F 5$\"0') F57$$\"07:r#4>+PF5$\"0;&45\"RT2*F57$$\"029jKrI+%F5$\"0c)R.DJV%*F57$$\" 0hOqHw3H%F5$\"0#[xS'\\Dr*F57$$\"0=],P>&[XF5$\"0tRBC!Q\"))*F57$$\"0$)pX w!)*\\[F5$\"0*GM*eJm)**F57$$\"0A7#))R)f(\\F5$\"0;uF\\a'****F57$$\"0N\" z,e%45&F5$\"0%*H8#[%Q***F57$$\"0Q%QL6'\\C&F5$\"0X!zg%3M'**F57$$\"0&=GZ 6\\(Q&F5$\"0>.T5$e2**F57$$\"0*H6560OcF5$\"0q%*=`qpu*F57$$\"06&f7\")*H! fF5$\"0D!zcUI\"[*F57$$\"0#o'3GP8:'F5$\"0Jag+1O9*F57$$\"0,?A;(4/kF5$\"0 9]*>-Q1()F57$$\"0yV%frEImF5$\"0yI9KA?B)F57$$\"0#=(H&egnoF5$\"0(z>sUmYw F57$$\"0O%[lng1rF5$\"0].*\\uPjpF57$$\"0M'35y?3tF5$\"0&[q*3(R6jF57$$\"0 7U=)G**=vF5$\"0nNCw^Mb&F57$$\"0Z^*=+'*GxF5$\"0>v'*RR(=ZF57$$\"0=U6K'\\ EzF5$\"0@\")GUE)eQF57$$\"0#*R,o>+6)F5$\"08Z:ZMM*HF57$$\"08!e/y\"[I)F5$ \"0EoRYAJ+#F57$$\"0s,e>=;Z)F5$\"0l]p5/^4\"F57$$\"0$\\-pe#4k)F5$\"0!zzz 1\"e:\"F-7$$\"0_)Q\\yN'y)F5$!0.?T.\"HKxF-7$$\"0h'eI&4l$*)F5$!0u?6L(oP< F57$$\"0X#Qi!=#p!*F5$!0T?f2L.j#F57$$\"0DvvA:*)>*F5$!0xq(*zd(RNF57$$\"0 94.VymJ*F5$!0g/\\UdwR%F57$$\"0X!QMSEI%*F5$!0I`Mw(\\a_F57$$\"0j,oin,`*F 5$!0enP6^A.'F57$$\"0zHo-'fA'*F5$!0\"Qc\\X8snF57$$\"0:!3`7W/(*F5$!0ZDT] kPW(F57$$\"0k][0d4x*F5$!0&>moc3,!)F57$$\"0r?%)yyo$)*F5$!0,jZrlOc)F57$$ \"0&\\7X,X'))*F5$!0:dq-lM**)F57$$\"0(*G+s%[H**F5$!0h\"pS`Jr$*F57$$\"0( [yvL9h**F5$!0:r+%)*4_'*F57$$\"09_]_P`)**F5$!0![=&e&Ho)*F57$$\"0)[1,1&p ***F5$!0O]qcmD(**F57$$\"01l!4>o****F5$!0Y-IIPr***F57$$\"0;%f.xh****F5$ !0*es2&fl***F57$$\"0iC&fU7(***F5$!0AI'e#GT(**F57$$\"0\")y1N4B***F5$!0z =K6b3$**F57$$\"0?0x^(ot**F5$!0w@numqVgcF57$$\"0?LO\"R\\t$*F5$!01Z6o?E#[F57$$\"00J^VheE*F5$!00B *)RxO-%F57$$\"0]-!\\pRP\"*F5$!0$GP.%*z.JF57$$\"0VCEe6^+*F5$!0_<\"f!yV> #F57$$\"0h!)H\\tU'))F5$!0Bx)zKrn7F57$$\"0N#)fg`yq)F5$!0&3aoKczGF-7$$\" 0G&e@&3bb)F5$\"0l\"=9-L(Q:F57$$\"0(4=ar\" 4?)F5$\"0fV6II1a#F57$$\"04T)Qh>?!)F5$\"0F`?h[bu#yF5$\" 0str0L\"*H%F57$$\"0hk7\"pUBwF5$\"0y`\")3j$[^F57$$\"0,*pYV$*GuF5$\"0E*p h_'p)eF57$$\"0/SgwwW@(F5$\"0>ii.sKi'F57$$\"0i(>]$yX*pF5$\"0v/mm*e&H(F5 7$$\"03Uq%F5$\"0b'='=Xx%**F57$ $\"0KM(\\!HmU%F5$\"08EuP(G5)*F57$$\"0K:ruUM7%F5$\"0$y$=jGfc*F57$$\"0(4 s_nMdQF5$\"0C!*oj#Gw#*F57$$\"0WlgJJxa$F5$\"0\"oy'onq&))F57$$\"0Gt.:wID $F5$\"0$R!*Q2?#Q)F57$$\"0H2\"z%=\"eHF5$\"0!=:c*e*QyF57$$\"0oVw\\u+m#F5 $\"0>'H(R;tA(F57$$\"0Sqe\"yW`BF5$\"0+QhAS*QlF57$$\"0Z)*4ide-#F5$\"0\\( QX++XdF57$$\"0\"*[ljtMs\"F5$\"0q_(Gtkl\\F57$$\"0(Q?9(yLU\"F5$\"0Q8^8&y aTF57$$\"0fVyrN65\"F5$\"0U!)p2-+D$F57$$\"0TZnMRkJ#F57$$ \"0PqjWr3)[F-$\"0oHAP5'f9F57$$\"0y$o5DLO9F-$\"0h:6C7yI%F-7$$!0u*H***zt W\"F-$!0:Ci9F4M%F-7$$!0\")o\\b1&=[F-$!0@Q?#p2T9F57$$!0*Hs3C'3.)F-$!0J` PyS&)Q#F57$$!0w#oe\"=#*3\"F5$!0\"Gz/Z'f@$F57$$!0$QBTn\"*49F5$!0(*QdCTw 6%F57$$!0VOdi_7t\"F5$!0\\jL**)>')\\F57$$!0Y5q(>C\\?F5$!05\"pgI].eF57$$ !0TkQEY@M#F5$!04(F57$$!0#el'=n=&HF5$ !0v,DUbn#yF57$$!0`F+k/lD$F5$!0#e!oxF\")Q)F57$$!0sD^7pjc$F5$!0v[g-$o%)) )F57$$!0kA8)))4OQF5$!0i@QRo-D*F57$$!0hjsope8%F5$!0;R%eyxx&*F57$$!0dK^$ [UKWF5$!0.t9kGS\")*F57$$!0-P]b'p8ZF5$!0w7.$pv^**F57$$!0+2f[n)R[F5$!0py TzyZ)**F57$$!08GO;S]'\\F5$!0B2]Ro#****F57$$!00RviZD6&F5$!0DJMzUB***F57 $$!0@yv4k&e_F5$!0O'H3`>f**F57$$!0oBC!=V-bF5$!0D!)31kM%)*F57$$!0))\\%G) )H!y&F5$!0(\\wPjn:'*F57$$!0&>*4Y03-'F5$!0XhowCAL*F57$$!01rH6C&yiF5$!0Y yATHc$*)F57$$!0PiGm-x^'F5$!0'HBE36y%)F57$$!0#zl.i_gnF5$!0;Tqzh?#zF57$$ !0%3I%>Ss(pF5$!09]Ye8^M(F57$$!07JniLS?(F5$!0O%*\\Vuql'F57$$!0k0ia7[;%\\^F57$$!0+&Q(o$oAyF5$!0%\\#> \"*z)>VF57$$!0y\"oP-q?!)F5$!0$3+t6rAMF57$$!0k@6!yC1#)F5$!0zgassN^#F57$ $!0hd=!H!zP)F5$!0>[&)\\d@h\"F57$$!0YI0oF#f&)F5$!0lUDkEf&fF-7$$!0%)4lwo Or)F5$\"0gS+J&fMKF-7$$!0a0EdH&p))F5$\"0[WaAM:I\"F57$$!0GW()*[c-!*F5$\" 0aQ_AVs<#F57$$!0t@&Rm%*Q\"*F5$\"0M,3QzY6$F57$$!0pJZ@/&e#*F5$\"0%e@#o4+ (RF57$$!03$4!zmUP*F5$\"0Mki`^%G[F57$$!08g=&RBy%*F5$\"0jfz^6^i&F57$$!0r \")zS3sd*F5$\"0Y;@%fN1kF57$$!0Idgg\"*Gm*F5$\"0X<)\\D'35(F57$$!0+-'3@kS (*F5$\"0BYB&4!eu(F57$$!0&[A#\\5y!)*F5$\"0$GjVYL9$)F57$$!0RaS%oug)*F5$ \"0tTMJ$))p()F57$$!0g<^&4,6**F5$\"04TyEt&3#*F57$$!04I:k1l%**F5$\"0:<\" )\\()>_*F57$$!0b1bGuW(**F5$\"0\"f\")y(\\5x*F57$$!0[^Fdo;***F5$\"0+ZoU+ ^#**F57$$!0u.DQlr***F5$\"0F!p$3)\\u**F57$$!0)G(o!*o(****F5$\"0ISfA?z** *F57$$!0>WRM&o****F5$\"0a1V@or***F57$$!0zJDvJu***F5$\"0f#=(o$*o(**F57$ $!0#[:t`E%)**F5$\"0^\\nH&oe)*F57$$!0ELt,TD'**F5$\"0Q(*R'3bk'*F57$$!0`X U[#=G**F5$\"020#[o\")f$*F57$$!0!o\\;%o'*))*F5$\"0;Tbpp:-*F57$$!0v)\\c= %e$)*F5$\"0V=^BPZb)F57$$!0]')QbDQx*F5$\"0c,S/``-)F57$$!0eRh:t?q*F5$\"0 (H7EJ6CuF57$$!019`WO4i*F5$\"07&yGjnenF57$$!0%*f()G%*R`*F5$\"0/g'\\U\\i gF57$$!0Z!3Nd=I%*F5$\"09614(*QD&F57$$!0*F5$\"0>p\"*zIN`$F57$$!0N1K!GUx!*F5$\"0JI]jtno#F57$$!06]e\\'zM* )F5$\"0XA.)HTEN')F5$! 09sH$e\"o\\\"F-7$$!0NHVG@`Y)F5$!01p/K./8\"F57$$!0Zhpg63I)F5$!0!HOsZCC? F57$$!08-5n%\\C\")F5$!03$>#z3C#HF57$$!0nT4h43#zF5$!0jsAh5Y)QF57$$!0s\\ rVC%GxF5$!0MlGmr4s%F57$$!0NlXCVS_(F5$!0=xq+)F57$$!0_wUa,]R'F5$!0>b#fQzB()F57$$!0*HxWYXlhF5$!0 Jb?_3<7*F57$$!0Z'***o^R*eF5$!0Q#HzT$>\\*F57$$!0KD`LrIk&F5$!0\"[r1\"Q7u *F57$$!05HWu(f*Q&F5$!00?Htil!**F57$$!006A#pa$)yp\\F5$!0,7pX`%****F57$$!0j8I]an#[ F5$!0l$H!f*>#)**F57$$!0d%3g#pJc%F5$!0j4OgT))))*F57$$!0V,\"**f!)yUF5$!0 (=\\Z=$Hq*F57$$!0.**HZYr*RF5$!0^7LG9pV*F57$$!0y(y^6^(o$F5$!05_='4'o0*F 57$$!0.>6VIiT$F5$!0i9,z3Rl)F57$$!0FdFy=65$F5$!012?#F5$!05q% )Q>e<'F57$$!05Bgpw1*=F5$!0_(4d\"*o,aF57$$!0`b3!H(*f:F5$!0[Yi(*p!GXF57$ $!0-(=\"[&>b7F5$!05viB$['o$F57$$!0pH5mJ<`*F-$!0%yF&pz[#GF57$$!0u\"oM-] $H'F-$!02fb6z!y=F57$$!0CtZI'pbIF-$!0UOw:wc:*F-7$$\"0D819PT?)!#C$\"0(R= U6ChC!#B-%'COLOURG6&%$RGBG$\"*++++\"!\")F(F(-%+AXESLABELSG6$Q!6\"Fa^o- %%VIEWG6$%(DEFAULTGFf^o" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 " nb2list:=proc(N,B) convert(N,base,B) end;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(nb2listGf*6$%\"NG%\"BG6\"F)F)-%(convertG6%9$%%baseG9 %F)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "nb2list(1212,2); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7-\"\"!F$\"\"\"F%F%F%F$F%F$F$F%" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "nb2list(1212,7);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7&\"\"\"\"\"&\"\"$F&" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 63 "list2nb:=proc(L,B) local i ;sum(L[i]*B^(i-1),i =1..nops(L)) end;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(list2nbGf*6$% \"LG%\"BG6#%\"iG6\"F+-%$sumG6$*&&9$6#8$\"\"\")9%,&F3F4F4!\"\"F4/F3;F4- %%nopsG6#F1F+F+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "sum(f( i),i=5..8);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,*-%\"fG6#\"\"&\"\"\"-F %6#\"\"'F(-F%6#\"\"(F(-F%6#\"\")F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "sum(f(i),i=3..18);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6 #,B-%\"fG6#\"\"$\"\"\"-F%6#\"\"%F(-F%6#\"\"&F(-F%6#\"\"'F(-F%6#\"\"(F( -F%6#\"\")F(-F%6#\"\"*F(-F%6#\"#5F(-F%6#\"#6F(-F%6#\"#7F(-F%6#\"#8F(-F %6#\"#9F(-F%6#\"#:F(-F%6#\"#;F(-F%6#\"# " 0 "" {MPLTEXT 1 0 17 "Sum(i^2,i=1..10);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$SumG6$*$)%\"iG\"\"#\"\"\"/F(;F*\"#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "sum(i^2,i=1..10);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"$&Q" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 " list2nb_inert:=proc(L,B) local i ;Sum(L[i]*B^(i-1),i=1..nops(L)) end; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%.list2nb_inertGf*6$%\"LG%\"BG6#% \"iG6\"F+-%$SumG6$*&&9$6#8$\"\"\")9%,&F3F4F4!\"\"F4/F3;F4-%%nopsG6#F1F +F+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "list2nb_inert([a0, a1,a2,a3,a4,a5,a6],B);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$SumG6$*&& 7)%#a0G%#a1G%#a2G%#a3G%#a4G%#a5G%#a6G6#%\"iG\"\"\")%\"BG,&F1F2F2!\"\"F 2/F1;F2\"\"(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "list2nb([a0 ,a1,a2,a3,a4,a5,a6],B);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,0%#a0G\"\" \"*&%#a1GF%%\"BGF%F%*&%#a2GF%)F(\"\"#F%F%*&%#a3GF%)F(\"\"$F%F%*&%#a4GF %)F(\"\"%F%F%*&%#a5GF%)F(\"\"&F%F%*&%#a6GF%)F(\"\"'F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "list2nb([1,5,3,3],7);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#\"%77" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "L2:=[a0,a1,a2,a3,a4,a5,a6];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%# L2G7)%#a0G%#a1G%#a2G%#a3G%#a4G%#a5G%#a6G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "whattype(L2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%%li stG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "ES2:=op(L2);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%$ES2G6)%#a0G%#a1G%#a2G%#a3G%#a4G%#a5 G%#a6G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "whattype(ES2);" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#%(exprseqG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 74 "randlist:=proc(l,m,M) local i, rd; rd:=rand(m..M): [seq(rd(),i=1..l)] end;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)randlis tGf*6%%\"lG%\"mG%\"MG6$%\"iG%#rdG6\"F-C$>8%-%%randG6#;9%9&7#-%$seqG6$- F0F-/8$;\"\"\"9$F-F-F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "?r and" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "roll:=rand(1..6):" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "seq(roll(),i=1..20);" }} {PARA 11 "" 1 "" {XPPMATH 20 "66\"\"&\"\"#F#\"\"'F$\"\"$\"\"%F'F%F#F& \"\"\"F#F$F&F$F$F'F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "d 2:=rand(3..20):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "seq(d2() ,i=1..15);" }}{PARA 11 "" 1 "" {XPPMATH 20 "61\"\"'\"\")F#F#\"#7\"#5\" \"%\"#=F'\"#8\"# " 0 "" {MPLTEXT 1 0 18 "seq(d2(),i=1..15);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 1\"\"*\"#8F$\"\"(\"#=F$\"\"'\"#5\"\"%F$F$\"\")F(F&F$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 74 "randlist:=proc(l,m,M) local i, rd; rd:=ra nd(m..M): [seq(rd(),i=1..l)] end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "randlist(30,7,20);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #7@\"#8\"#:\"#5\"#;\"\"*\"\")F%\"\"(F*\"#6F)F&\"#>F&\"#?F*\"#7F(F*\"#< F$F)\"#=F*F+F'F(F'F&F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "r andlist(30,1,2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7@\"\"#F$\"\"\"F$F %F$F%F$F%F$F$F%F%F%F$F%F%F%F%F$F%F$F$F$F$F$F%F%F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 149 "brline:=proc(L,x) if x<0 then 0 elif x<1 then L[1]*x elif x%'brlineGf*6$%\"LG%\"xG6\"F)F)@)29%\"\"!F-2F,\"\"\"*&&9$6#F/F/F ,F/2F,-%%nopsG6#F2,&*&,&&F26#,&-%&floorG6#F,F/F/F/F/&F26#F>!\"\"F/,&F, F/F>FCF/F/FAF/&F26#F5F)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "L4:=[1,2,1,0,1,2,3,2,1];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#L4G 7+\"\"\"\"\"#F&\"\"!F&F'\"\"$F'F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "plot(x->brline(L4,x),-1..9);" }}{PARA 13 "" 1 "" {GLPLOT2D 494 494 494 {PLOTDATA 2 "6%-%'CURVESG6$7^y7$!\"\"$\"\"!F*7$$ !+)\\RUZ*!#5F)7$$!+'4yn,*F.F)7$$!+0\\J-&)F.F)7$$!+=:W%)zF.F)7$$!+$\\H! puF.F)7$$!+ol<\"*pF.F)7$$!+VvQ'\\'F.F)7$$!+Dgn%)fF.F)7$$!+tbguaF.F)7$$ !+F.F)7$$!+y%>0[\"F.F)7$$!*MQ&[%*F.F)7$$!*v* )pq%F.F)7$$!+)=KkS$!#6F)7$$!+DY(e5#FboF)7$$!+Wefb9FboF)7$$!+D1<`!)!#7F )7$$!+=nx,[F\\pF)7$$!+7GQ]:F\\pF)7$$\"+%465q\"F\\pFdp7$$\"(0C&\\!\"*Fg p7$$\"+]s6sHFboF[q7$$\")S**[aFipF^q7$$\"*hr<1\"FipFaq7$$\"*k@k`\"FipFd q7$$\"*$eR[?FipFgq7$$\"*7$>!e#FipFjq7$$\"*BCJ/$FipF]r7$$\"*]-Ja$FipF`r 7$$\"*)*G'fSFipFcr7$$\"*Q\\\\c%FipFfr7$$\"*%G(Q0&FipFir7$$\"*)*Qnf&Fip F\\s7$$\"*OGX3'FipF_s7$$\"*kZ`g'FipFbs7$$\"*J(GxqFipFes7$$\"*.UKf(FipF hs7$$\"*@:(y!)FipF[t7$$\"*duhe)FipF^t7$$\"*%)3B3*FipFat7$$\"*X:55FipFgt7$$\"+$Ra81\"FipFjt7$$\"+)f)376FipF]u7$$\"+k!3(e6Fi pF`u7$$\"+L#R@@\"FipFcu7$$\"+2(G*f7FipFfu7$$\"+bA)3J\"FipFiu7$$\"+,8lf 8FipF\\v7$$\"+fI!QT\"FipF_v7$$\"+.Xpg9FipFbv7$$\"+6n\"R^\"FipFev7$$\"+ wHUi:FipFhv7$$\"+17[:;FipF[w7$$\"+'[h7m\"FipF^w7$$\"+\"))*R8T7>FipF]x7$$ \"+)\\]%Q>FipF`x7$$\"+A!*[k>FipFcx7$$\"+Bt*o(>FipFfx7$$\"+CcI*)>FipFix 7$$\"+u(4b*>FipF\\y7$$\"+DRr,?Fip$\"+vgG)*>Fip7$$\"+w!=z+#Fip$\"+C>3#* >Fip7$$\"+EA79?Fip$\"+ux(e)>Fip7$$\"+I0CS?Fip$\"+q%f(f>Fip7$$\"+N)ej1# Fip$\"+l6kL>Fip7$$\"+Ybk8@Fip$\"+aWN')=Fip7$$\"+8i!f;#Fip$\"+(y$4M=Fip 7$$\"+EG'f@#Fip$\"+ur.%y\"Fip7$$\"+*f(*eE#Fip$\"+,C5Mo\"Fip7$$\"+CK4mBFip$\"+wn!Rj\"Fip7$$\"+!G\"H:CFip$\"+?(3Ze\" Fip7$$\"+\"y6'pCFip$\"+>#)QI:Fip7$$\"+XXz=DFip$\"+ba?\"[\"Fip7$$\"+LJ4 pDFip$\"+no!4V\"Fip7$$\"+-bC?EFip$\"+)\\a(z8Fip7$$\"+$[ksm#Fip$\"+&Q!H_Fip$\" +]!>!H7Fip7$$\"+nk@!G&Fip$\"+nk@!G\"Fip7$$\"+'>'RL`Fip$\"+'>'RL8Fip7$$ \"+1$*oz`Fip$\"+1$*oz8Fip7$$\"+NroHaFip$\"+NroH9Fip7$$\"+%yR8[&Fip$\"+ %yR8[\"Fip7$$\"+C=(=`&Fip$\"+C=(=`\"Fip7$$\"+rTw!e&Fip$\"+rTw!e\"Fip7$ $\"+%y]]j&Fip$\"+%y]]j\"Fip7$$\"+=(HQo&Fip$\"+=(HQo\"Fip7$$\"+[;\"ft&F ip$\"+[;\"ft\"Fip7$$\"+=c5$y&Fip$\"+=c5$y\"Fip7$$\"+&3,Z$eFip$\"+&3,Z$ =Fip7$$\"+2%[K)eFip$\"+2%[K)=Fip7$$\"+UV*R$fFip$\"+UV*R$>Fip7$$\"+pxg$ )fFip$\"+pxg$)>Fip7$$\"+K%[b.'Fip$\"+K%[b.#Fip7$$\"+dMd&3'Fip$\"+dMd&3 #Fip7$$\"+w7tOhFip$\"+w7tO@Fip7$$\"+#[lu='Fip$\"+#[lu=#Fip7$$\"+]\\3Mi Fip$\"+]\\3MAFip7$$\"+:h^(G'Fip$\"+:h^(G#Fip7$$\"+$f0`L'Fip$\"+$f0`L#F ip7$$\"+S\"fiQ'Fip$\"+S\"fiQ#Fip7$$\"+'=G]V'Fip$\"+'=G]V#Fip7$$\"+X*z \"*['Fip$\"+X*z\"*[#Fip7$$\"+(Qrg`'Fip$\"+(Qrg`#Fip7$$\"+)f$H*e'Fip$\" +)f$H*e#Fip7$$\"+f)*zPmFip$\"+f)*zPEFip7$$\"+!4e3p'Fip$\"+!4e3p#Fip7$$ \"+s$Qmt'Fip$\"+s$Qmt#Fip7$$\"+knx)y'Fip$\"+knx)y#Fip7$$\"+z)R\"RoFip$ \"+z)R\"RGFip7$$\"+&4q%*)oFip$\"+&4q%*)GFip7$$\"+c^hRpFip$\"+c^hRHFip7 $$\"+5?qjpFip$\"+5?qjHFip7$$\"+f))y()pFip$\"+f))y()HFip7$$\"+!\\)H%*pF ip$\"+!\\)H%*HFip7$$\"+?\"33+(Fip$\"+!)=>**HFip7$$\"+]xJ2qFip$\"+]Ao#* HFip7$$\"+!QFQ,(Fip$\"+?E<')HFip7$$\"+Sm%o-(Fip$\"+gL:tHFip7$$\"+/f')R qFip$\"+'4M,'HFip7$$\"+5\"*\\*3(Fip$\"+!*3]5HFip7$$\"+=dtTrFip$\"+#Gk# eGFip7$$\"+KC-*=(Fip$\"+ov(4\"GFip7$$\"+&4$GTsFip$\"+0preFFip7$$\"+3(R 8H(Fip$\"+#Hg'3FFip7$$\"+#[u7M(Fip$\"+=bseEFip7$$\"+[:V$R(Fip$\"+_%olg #Fip7$$\"+5,ZTuFip$\"+!*)H&eDFip7$$\"+m\"o1\\(Fip$\"+M=L4DFip7$$\"+j') )\\a(Fip$\"+P8,bCFip7$$\"+F9<%f(Fip$\"+t&GeS#Fip7$$\"+?+ZWwFip$\"+!)*H bN#Fip7$$\"+(QAcp(Fip$\"+8wP/BFip7$$\"+n8kUxFip$\"+L'etD#Fip7$$\"+!3iF z(Fip$\"+?zB2AFip7$$\"+m7]UyFip$\"+M()\\d@Fip7$$\"+Qnq&*yFip$\"+iKH/@F ip7$$\"+h#eE%zFip$\"+RFip7$$\"+#Q(3%4)Fip$\"+=E\"f!>Fip7$$\"+\"=,h9)Fip$\"+>))* Q&=Fip7$$\"+#QD$)>)Fip$\"+=Yn,=Fip7$$\"+y;%eC)Fip$\"+A$eTv\"Fip7$$\"+p =I'H)Fip$\"+J\")p.X\"Fip7$$\"+rhU(f)Fip$\"+HQd-9Fip7$$\"+!*R&ok)Fip$ \"+5g9`8Fip7$$\"+OsE(p)Fip$\"+kFt-8Fip7$$\"+KWq]()Fip$\"+obH\\7Fip7$$ \"+56q*z)Fip$\"+!*))H+7Fip7$$\"+?r1[))Fip$\"+!)G$>:\"Fip7$$\"+$fp(**)) Fip$\"+2/B+6Fip7$$\"+2&f8&*)Fip$\"+$\\S'[5Fip7$\"\"*$\"\"\"F*-%'COLOUR G6&%$RGBG$\"*++++\"!\")F)F)-%+AXESLABELSG6$Q!6\"Fiin-%%VIEWG6$;$F(F*$F \\inF*%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "with(Strin gTools):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "iverson:=proc(P) if evalb(P)=true t hen 1 else 0 fi end;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(iversonGf*6 #%\"PG6\"F(F(@%/-%&evalbG6#9$%%trueG\"\"\"\"\"!F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "iverson(1=0);iverson(1=1);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "evalb(1=1);" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#%%trueG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "with(StringTools):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 94 "CFW:=proc(w,x) if w=\"\" then 0 else CFW(w[1..length( w)-1],x)+iverson(w[length(w)]=x) fi end; " }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$CFWGf*6$%\"wG%\"xG6\"F)F)@%/9$Q!F)\"\"!,&-F$6$&F,6#; \"\"\",&-%'lengthG6#F,F5F5!\"\"9%F5-%(iversonG6#/&F,6#F7F;F5F)F)F)" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "CFW(\"aabab\",\"a\");" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "w:=\"aaababbabab\":seq(w[1..k],k=1..length(w));" }} {PARA 12 "" 1 "" {XPPMATH 20 "6-Q\"a6\"Q#aaF$Q$aaaF$Q%aaabF$Q&aaabaF$Q 'aaababF$Q(aaababbF$Q)aaababbaF$Q*aaababbabF$Q+aaababbabaF$Q,aaababbab abF$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "w:=\"aaababbabab\": seq(CFW(w[1..k],\"a\")-CFW(w[1..k],\"b\"),k=1..length(w));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6-\"\"\"\"\"#\"\"$F$F%F$F#F$F#F$F#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "W2L:=proc(w) [seq(CFW(w[1..k],\"a\" )-CFW(w[1..k],\"b\"),k=1..length(w))] end;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$W2LGf*6#%\"wG6\"F(F(7#-%$seqG6$,&-%$CFWG6$&9$6#;\"\" \"%\"kGQ\"aF(F5-F/6$F1Q\"bF(!\"\"/F6;F5-%'lengthG6#F2F(F(F(" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "W2L(\"aaababbababb\");" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#7.\"\"\"\"\"#\"\"$F%F&F%F$F%F$F%F$\"\" !" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 44 "D\351finition : Un mot de Dy ck est un mot dont " }}{PARA 0 "" 0 "" {TEXT -1 25 "1) la liste est po sitive " }}{PARA 0 "" 0 "" {TEXT -1 44 "2) se termine \340 0 (autant d e \"a\" que de \"b\")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 154 "isd yck:=proc(w) local N,res,k,L:N:=length(w):L:=W2L(w):res:=1:for k to N \+ while res=1 do if L[k]<0 then res:=0 else fi od: min(res,iverson(L[N]= 0)) end; " }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%'isdyckGf*6#%\"wG6&% \"NG%$resG%\"kG%\"LG6\"F-C'>8$-%'lengthG6#9$>8'-%$W2LGF3>8%\"\"\"?(8&F ;F;F0/F:F;@%2&F66#F=\"\"!>F:FCF--%$minG6$F:-%(iversonG6#/&F66#F0FCF-F- F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "isdyck(\"aaababbababb \");" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 25 "isdyck(\"aaababbababbba\");" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 104 "randword:=proc(l,A) loca l res,i; res:=\"\": for i to l do res:=cat(res,A[rand(1..nops(A))()]) \+ od :res end;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%)randwordGf*6$%\"lG% \"AG6$%$resG%\"iG6\"F,C%>8$Q!F,?(8%\"\"\"F39$%%trueG>F/-%$catG6$F/&9%6 #--%%randG6#;F3-%%nopsG6#F;F,F/F,F,F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "randword(10,[a,b]);" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#Q+ababababbb6\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "LL:=NU LL:for i to 100 do LL:=LL,randword(6,[a,b]) od:L3:=[LL];" }}{PARA 12 " " 1 "" {XPPMATH 20 "6#>%#L3G7`qQ'babaab6\"Q'aabaabF'Q'abbbabF'Q'bbabbb F'Q'aabbabF'Q'aaaaabF'Q'aaabaaF'Q'abbabaF'Q'baaabbF'Q'bbbbbbF'Q'baabba F'Q'bbaabaF'Q'bbbbabF'Q'abaabbF'Q'bbaaabF'F1Q'abaaabF'F4Q'abaaaaF'Q'ab ababF'Q'aaababF'Q'babbabF'Q'aaabbaF'F9Q'abbabbF'Q'baaaaaF'Q'babaaaF'F0 Q'aaaaaaF'Q'bbbaabF'Q'abbaabF'F=Q'baaaabF'Q'aababaF'F8Q'aabbaaF'Q'aaba aaF'Q'bbababF'Q'aaaabbF'Q'aaaabaF'Q'bbbbbaF'F4FAF2FFF(Q'bbaaaaF'F5Q'bb babbF'Q'bbbaaaF'F;F)Q'baaabaF'F&Q'aabbbbF'Q'bbaabbF'F4F8Q'bababaF'Q'ab bbbbF'F7F5F6F8FDQ'bababbF'F1F0F,F,F2Q'ababaaF'FAF*Q'aabbbaF'FBF0Q'abba aaF'F=Q'ababbbF'Q'bbabbaF'FRFCFIF&Q'baababF'FXFGF(FEF@F+Q'aaabbbF'F)F. F2FNQ'bbbabaF'Q'babbaaF'Q'aababbF'" }}}{EXCHG {PARA 12 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "map(x->isdyck(x), L3);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7`q\"\"!F$F$F$\"\"\"F$F$F$F$F$ F$F$F$F%F$F$F$F%F$F%F$F$F$F$F$F$F$F$F$F$F$F$F$F$F%F$F$F$F$F$F$F%F$F$F$ F$F$F$F$F$F$F$F$F$F$F$F%F%F$F$F$F$F$F%F$F$F$F$F$F$F$F$F$F$F$F$F$F$F$F$ F$F$F$F$F$F$F$F$F$F$F$F%F%F$F$F$F$F$F$F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "map(x->[x,isdyck(x)],L3);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7`q7$Q'babaab6\"\"\"!7$Q'aabaabF&F'7$Q'abbbabF&F'7$Q'bb abbbF&F'7$Q'aabbabF&\"\"\"7$Q'aaaaabF&F'7$Q'aaabaaF&F'7$Q'abbabaF&F'7$ Q'baaabbF&F'7$Q'bbbbbbF&F'7$Q'baabbaF&F'7$Q'bbaabaF&F'7$Q'bbbbabF&F'7$ Q'abaabbF&F07$Q'bbaaabF&F'F;7$Q'abaaabF&F'FA7$Q'abaaaaF&F'7$Q'abababF& F07$Q'aaababF&F'7$Q'babbabF&F'7$Q'aaabbaF&F'FK7$Q'abbabbF&F'7$Q'baaaaa F&F'7$Q'babaaaF&F'F97$Q'aaaaaaF&F'7$Q'bbbaabF&F'7$Q'abbaabF&F'FS7$Q'ba aaabF&F'7$Q'aababaF&F'FI7$Q'aabbaaF&F'7$Q'aabaaaF&F'7$Q'bbababF&F'7$Q' aaaabbF&F'7$Q'aaaabaF&F'7$Q'bbbbbaF&F'FAFenF=F_oF(7$Q'bbaaaaF&F'FC7$Q' bbbabbF&F'7$Q'bbbaaaF&F'FOF*7$Q'baaabaF&F'F$7$Q'aabbbbF&F'7$Q'bbaabbF& F'FAFI7$Q'bababaF&F'7$Q'abbbbbF&F'FGFCFEFIF[o7$Q'bababbF&F'F;F9F1F1F=7 $Q'ababaaF&F'FenF,7$Q'aabbbaF&F'FgnF97$Q'abbaaaF&F'FS7$Q'ababbbF&F'7$Q 'bbabbaF&F'FgpFinFeoF$7$Q'baababF&F'FcqFaoF(F]oFYF.7$Q'aaabbbF&F0F*F5F =F_p7$Q'bbbabaF&F'7$Q'babbaaF&F'7$Q'aababbF&F0" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "36 0 0" 0 }{VIEWOPTS 1 1 0 3 2 1804 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }